How do you evaluate √50 - √ 8?

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Answer 1 · 2015-11-04T11:57:28

#3sqrt(2)#

It is a matter of splitting up the numbers (partitioning) into squares. These squares can then be taken out of the root.

In this case

#8=2 times 4 = 2 times 2^2#
#50 =2 times 25 = 2 times 5^2#

So we can now write the expression as:

#sqrt(2 times 5^2) - sqrt(2 times 2^2)#

#5sqrt(2) -2sqrt(2)#

#color(blue)("Now the expression is behaving as if the "sqrt(2))# #color(blue)("is a unit of measurement")#.

As both have the same "units" we can subtract them directly. Thus we have:

#(5-2)sqrt(2) = 3sqrt(2)#